000			01862nam a22002297a 4500
999			_c55795 _d55795
005			20191022140104.0
008			191022b ||||| |||| 00| 0 eng d
020			_a978147044890
082			_a512.74 POL
100			_aPollack, Paul,
245			_aA conversational introduction to algebraic number theory _b : arithmetic beyond Z _c/ Paul Pollack
260			_aProvidence, Rhode Island _b : AMS, American Mathematical Society, _c©2017
300			_aix, 316 pages _b: illustrations _c ; 22 cm.
490			_aStudent mathematical library, v. 84.
505			_aGetting our feet wetCast of charactersQuadratic number fields: First stepsParadise lost--and foundEuclidean quadratic fieldsIdeal theory for quadratic fieldsPrime ideals in quadratic number ringsUnits in quadratic number ringsA touch of classMeasuring the failure of unique factorizationEuler's prime-producing polynomial and the criterion of Frobenius-RabinowitschInterlude: Lattice pointsBack to basics: Starting over with arbitrary number fieldsIntegral bases: From theory to practice, and backIdeal theory in general number ringsFiniteness of the class group and the arithmetic of $\overline{\mathbb{Z}}$Prime decomposition in general number ringsDirichlet's units theorem, IA case study: Units in $\mathbb{Z}[\sqrt[3]{2}]$ and the Diophantine equation $X^3-2Y^3=\pm1$Dirichlet's units theorem, IIMore Minkowski magic, with a cameo appearance by HermiteDedekind's discriminant theoremThe quadratic Gauss sumIdeal density in quadratic number fieldsDirichlet's class number formulaThree miraculous appearances of quadratic class numbersIndex.
650			_aMathematics
650			_aAlgebra
650			_aAlgebraic number theory.
650			_aNumber theory -- Algebraic number theory: global fields -- Algebraic number theory: global fields.
700			_a Pollack, Paul,
942			_cMDL